Block #2,932,199

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/20/2018, 11:33:46 PM · Difficulty 11.4003 · 3,899,471 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
a02c5a9e6525ea76aa1f93339a88a6f8749e3b1a99f5d6d61fe941d41969866c

Height

#2,932,199

Difficulty

11.400266

Transactions

2

Size

426 B

Version

2

Bits

0b6677d1

Nonce

41,467,065

Timestamp

11/20/2018, 11:33:46 PM

Confirmations

3,899,471

Merkle Root

7860812098785dfc4bc60467884278c5eb925d805c0c6cfc6bcc86d633ca2cba
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.704 × 10⁹⁴(95-digit number)
17047648700892759078…01538587913055221601
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.704 × 10⁹⁴(95-digit number)
17047648700892759078…01538587913055221601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.409 × 10⁹⁴(95-digit number)
34095297401785518156…03077175826110443201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.819 × 10⁹⁴(95-digit number)
68190594803571036312…06154351652220886401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.363 × 10⁹⁵(96-digit number)
13638118960714207262…12308703304441772801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.727 × 10⁹⁵(96-digit number)
27276237921428414525…24617406608883545601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.455 × 10⁹⁵(96-digit number)
54552475842856829050…49234813217767091201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.091 × 10⁹⁶(97-digit number)
10910495168571365810…98469626435534182401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.182 × 10⁹⁶(97-digit number)
21820990337142731620…96939252871068364801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.364 × 10⁹⁶(97-digit number)
43641980674285463240…93878505742136729601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.728 × 10⁹⁶(97-digit number)
87283961348570926480…87757011484273459201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.745 × 10⁹⁷(98-digit number)
17456792269714185296…75514022968546918401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,897,465 XPM·at block #6,831,669 · updates every 60s
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